The quantities which have the same dimensions as those of solid angle are:
1. stress and angle
2. strain and arc
3. angular speed and stress
4. strain and angle
Subtopic:  Dimensions |
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In a vernier callipers, \((N+1)\) divisions of the vernier scale coincide with \(N\) divisions of the main scale. If \(1\) \(\text{MSD}\) represents \(0.1~\text{mm}\), the vernier constant (in \(\text{cm}\)) is:
1. \(\dfrac{1}{100(N+1)} \) 2. \(100N\)
3. \(10(N+1) \) 4. \(\dfrac{1}{10 N}\)
Subtopic:  Measurement & Measuring Devices |
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A force defined by; \(F = \alpha t^2 + \beta t\) acts on a particle at a given time \(t.\) The factor which is dimensionless, if \(\alpha\) and \(\beta\) are constants, is: 
1. \(\alpha t / \beta \) 2. \(\alpha \beta t \)
3. \(\alpha \beta / t \) 4. \(\beta t / \alpha\)
Subtopic:  Dimensions |
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The percentage errors in the measurement of mass and momentum of an object are \(1\%\) and \(2\%\) respectively. The percentage error in the measurement of kinetic energy of the object will be:
1. \(1\%\)
2. \(3\%\)
3. \(4\%\)
4. \(5\%\)
Subtopic:  Errors |
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Match List- I with List- II.
List-I 
(Measured values)
List-II 
(Significant figures)
A. \(0.001213\) I. \(2\)
B. \(2.1 \times 10^{16} \) II. \(3\)
C. \(3.70\) III. \(1\)
D. \(3000\) IV. \(4\)
 
Choose the correct answer from the options given below:
1. A-III, B-II, C-I, D-IV
2. A-III, B-I, CII, D-IV
3. A-I, B-II, C-IV, D-III
4. A-IV, B-I, C-II, D-III
Subtopic:  Significant Figures |
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A vernier calipers has \(1~\text{mm}\) marks on the main scale. It has \(20\) equal divisions on the vernier scale which match with \(16\) main scale divisions. The least count of this vernier calipers is:
1. \(0.02~\text{mm}\) 2. \(0.05~\text{mm}\)
3. \(0.10~\text{mm}\) 4. \(0.20~\text{mm}\)
Subtopic:  Measurement & Measuring Devices |
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The pitch of an error-free screw gauge is \(1~\text{mm},\) and there are \(100\) divisions on the circular scale. While measuring the diameter of a thick wire, the pitch scale reads \(1~\text{mm},\) and \(63^\text{rd}\) division on the circular scale coincides with the reference line. The diameter of the wire is:
1. \(1.63 ~\text{cm}\)
2. \(0.163 ~\text{cm}\)
3. \(0.163~\text m\)
4. \(1.63 ~\text m\)
Subtopic:  Measurement & Measuring Devices |
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The potential energy of a particle moving along the \(x\text-\)direction varies as \({V}=\dfrac{{A}x^{2}}{\sqrt{x}+{B}}.\) The dimensions of \(\dfrac{A^2}{B}\) are:
1. \([{M}^{3/2}{L}^{1/2}{T}^{-3}]\)
2. \([M^{1/2}LT^{-3}]\)
3. \([{M}^2{L}^{1/2}{T}^{-4}]\)
4. \([ML^{2}T^{-4}]\)
Subtopic:  Dimensions |
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A metal wire has mass \((0.4\pm 0.002)~\text{g}\), radius \((0.3\pm 0.001)~\text{mm}\) and length \((5\pm 0.02)~\text{cm}\). The maximum possible percentage error in the measurement of density will nearly be:
1. \(1.4 \%\)
2. \(1.2 \%\)
3. \(1.3 \%\)
4. \(1.6 \%\)
Subtopic:  Errors |
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The errors in the measurement which arise due to unpredictable fluctuations in temperature and voltage supply are:
1. Random errors
2. Instrumental errors
3. Personal errors
4. Least count errors
Subtopic:  Errors |
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